<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied to deal with fractional telegraph differential equation defined by Caputo fractional derivative for fractional orders <italic>α</italic> = 1.1, 1.5, 1.9. Numerical results confirm the accuracy and effectiveness of the technique.</p></abstract>

The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied to deal with fractional telegraph differential equation defined by Caputo fractional derivative for fractional orders α = 1.1, 1.5, 1.9. Numerical results confirm the accuracy and effectiveness of the technique.

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Faculty of Arts and Sciences, Department of Mathematics

Art and Science Faculty, Department Of Mathematics

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are...

$τ = \frac{1}{N}, h = \frac{pi}{M}$ \tau = {1 \over N},\,h = {{pi} \over M}
The difference scheme (8)			In method [13]
	α
N = M = 40	1.5	0.0040	0.0242
N = M = 80	1.5	5.4707 × 10⁻⁴	0.0118
N = M = 160	1.5	0.0022	0.0058
N = 100, M = 10	1.1	7.0178 × 10⁻⁴
	1.5	0.0045
	1.9	0.0093
N = 225,M = 15	1.1	3.4496 × 10⁻⁴
	1.5	0.0040
	1.9	0.0083
N = 400,M = 20	1.1	2.0762 × 10⁻⁴
	1.5	0.0034
	1.9	0.0079

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Data publikacji: 31 mar 2020

Zakres stron: 163 - 170

Otrzymano: 24 mar 2019

Przyjęty: 15 maj 2019

DOI: https://doi.org/10.2478/amns.2020.1.00015

Słowa kluczowe
Fractional order Telegraph Partial Differential equations, Finite Difference Method, Stability

© 2020 Mahmut Modanli et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Error Analysis

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Data publikacji: 31 mar 2020

Zakres stron: 163 - 170

Otrzymano: 24 mar 2019

Przyjęty: 15 maj 2019

DOI: https://doi.org/10.2478/amns.2020.1.00015

Słowa kluczoweFractional order Telegraph Partial Differential equations, Finite Difference Method, Stability

© 2020 Mahmut Modanli et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Error Analysis

Słowa kluczowe
Fractional order Telegraph Partial Differential equations, Finite Difference Method, Stability